On the adjunction process over a surface in char p.
On the adjunction process over a surface in char. p II: the singular case.
On the analogue of the division polynomials for hyperelliptic curves.
On the arithmetic Chern character
We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern class of the sequence and its Chern character with support on the finite fibers.Next, we compute these classes in the situation encountered by the second author when proving a “Kodaira vanishing theorem” for arithmetic...
On the Arithmetic of Abelian Varieties.
On the arithmetic of an elliptic curve over a -extension
On the arithmetic of genus two fibrations
On the arithmetic of J0 (N) new.
On the Arithmetic of Special Values of L Functions.
On the automorphisms of surfaces of general type in positive characteristic
Here we give an explicit polynomial bound (in term of and not depending on the prime ) for the order of the automorphism group of a minimal surface of general type defined over a field of characteristic .
On the automorphisms of surfaces of general type in positive characteristic, II
Here we give an upper polynomial bound (as function of but independent on ) for the order of a -subgroup of with minimal surface of general type defined over the field with . Then we discuss the non existence of similar bounds for the dimension as -vector space of the structural sheaf of the scheme .
On the average value of the canonical height in higher dimensional families of elliptic curves
Given an elliptic curve E over a function field K = ℚ(T₁,...,Tₙ), we study the behavior of the canonical height of the specialized elliptic curve with respect to the height of ω ∈ ℚⁿ. We prove that there exists a uniform nonzero lower bound for the average of the quotient over all nontorsion P ∈ E(K).
On the behavior of Igusa,'s local zeta function in towers of field extension
On the Birch and Swinnerton-Dyer Conjecture.
On the Classification of Commutative Formal Group Laws over p-Hilbert Domains and a Finiteness Theorem for Higher Hasse-Witt Matrices.
On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field
On the conductor formula of Bloch
In [6], S. Bloch conjectures a formula for the Artin conductor of the ℓ-adic etale cohomology of a regular model of a variety over a local field and proves it for a curve. The formula, which we call the conductor formula of Bloch, enables us to compute the conductor that measures the wild ramification by using the sheaf of differential 1-forms. In this paper, we prove the formula in arbitrary dimension under the assumption that the reduced closed fiber has normal crossings.
On the congruence properties of the zeta function of algebraic varieties.
On the Conjecture of Birch and Swinnerton-Dyer
On the conjecture of Birch and Swinnerton-Dyer for abelian varieties over function fields in characteristic p > 0.